Gravitation
Universal Law of Gravitation F = G m1m2 / r2 Gravitational Force is independent of the medium . The gravitational force inside a body is zero . Gravitational Constant G = 6.67 x 10-11 Nm2/kg2 Acceleration due to Gravity Variation with Height g = GM / (R+h)2 gh = g (R/(R+h)2) gh = g (1 - 2h/R) Variation with Depth g = gh(1 - d/R) for every percentage decrease in radius , with mass constant ; there is 2 % increase in acceleration due to gravity Variation with Latitude g' = g - Rω2cos2Φ Relation between Variation of height and depth ''' If acceleration due to gravity is same at a certain height and depth ; then d = 2h Gravitational Field Intensity Gravitational field is the field of attraction around a mass . Gravitational Field Intensity is the amount of Force experienced by an object of unit mass in a gravitational Field . ... Intensity = Force / mass Gravitational Potential Energy Gravitational Potential Energy is the work done in bringing a charge of unit mass from infinity to a point against the gravitational field . Potential Energy (U) = Force . Displacement = - GMm /r ... U = Vm Gravitational Potential Gravitational potential is the amount of work done per unit mass in a gravitational field . Potential(V) = - GM / r ... V = U / m Gravitational Potential is always directed opposite to Gravitational Field . '''Cases of Potential : # Due to point mass : V = - GM/r ... at r = 0 , Z is negative infinite . The graph will be negative , curved and parallel to V and r axes . # Inside a Solid Sphere : '''V = - GM (1.5R2 - 0.5r2) / R3 . At r=R ,V = - GM/'R . At r = 0 ,V = -1.5GM'/'R The graph is negative , parabolic . # '''Outside a Solid Sphere : '''V = -GM/r , at r = infinity , V = 0 ; On surface , V = -GM/R # '''Due to a Spherical Shell : '''Outside ' V = -GM/r . Inside V = - GM/r # '''On the Axis of a Ring : '''V = - GM / sqrt(R2+x2) Kepler's Laws '''Law of Orbits Kepler's Law of Orbits states that all planets revolve around the sun in elliptical orbits with sun as the focus . Law of Areas Kepler's Law of Areas states that a planet sweeps equal Areas in equal intervals of time around the sun . Law of Periods Kepler's Law of Periods states that the square of Time Period is directly proportional to the cube of Distance . ... T2 α r3 Rocket Science Critical Velocity vc = sqrt (GM/r) vc = sqrt (ghr) Time Period T = 2π sqrt (r3 / GM) Binding Energy B.E. = - T.E. B.E. = GMm / r {At rest} B.E. = (GMm) / 2r Escape Velocity ve = sqrt (2ghr) ve = sqrt (2GM/r) The escape velocity remains independent of angle of projection . Escape Velocity for an object on earth is 11.2 km/s Tips and Tricks Category:Physics